While three watchmen were guarding an orchard, a thief slipped in a stole some apples. On his way out, he met the three watchmen one after another, and to each in turn he gave half the apples he had and two besides. In this way he managed to escape with one apple. How many had he stolen originally?
 

Dear Student,

Please find below the solution to the asked query:

Let total number of apples stolen =  x 

Step 1 ) From given condition apples given to first watchman  = x2 + 2 = x + 42
Then ,

Apples remained with thief  = x - x + 42 = 2 x - x - 42 = x - 42

Step 2 ) From given condition apples given to second watchman  = x - 422 +2  = x - 44 +2 = x - 4 + 84 = x + 44
Then ,

Apples remained with thief  = x - 42 - x + 44 = 2 x - 8 - x - 44 = x - 124

Step 3 ) From given condition apples given to third watchman  = x - 1242 +2  = x - 128 +2 = x - 12 + 168 = x + 48
Then ,

Apples remained with thief at last  = x - 124 - x + 48 = 2 x - 24 - x - 48 = x - 288

Also given at last thief have one apple , So

x - 288 = 1x - 28 = 8x = 36

Therefore,

Total number of apples stolen = 36                                                       ( Ans )


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